Geometry Level 3

Let $$A_1B_1C_1D_1A_2B_2C_2D_2$$ be a unit cube, where the vertex $$X_2$$ is vertically above the vertex $$X_1$$. Let $$M$$ be the center of face $$A_2 B_2 C_2 D_2$$. Rectangular pyramid $$MA_1B_1C_1D_1$$ is cut out of the cube. The surface area of the solid that remains after the pyramid is removed is expressed in the form $$a + \sqrt{b}$$, where $$a$$ and $$b$$ are positive integers and $$b$$ is not divisible by the square of any prime. What is $$a+b$$?

This problem is posed by Muhammad A.

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